The Global Dimension of Schur Algebras for GL_2 and GL_3

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dc.creatorParker, Alison E.
dc.date2005-07-26
dc.date.accessioned2026-07-07T05:21:59Z
dc.date.available2026-07-07T05:21:59Z
dc.descriptionWe first define the notion of good filtration dimension and Weyl filtration dimension in a quasi-hereditary algebra. We calculate these dimensions explicitly for all irreducible modules in SL_2 and SL_3. We use these to show that the global dimension of a Schur algebra for GL_2 and GL_3 is twice the good filtration dimension. To do this for SL_3, we give an explicit filtration of the modules \nabla(λ) by modules of the form \nabla(μ)^F \otimes L(ν) where μis a dominant weight and νis p-restricted.
dc.descriptionuses xypic v 3.7 and amsart v. 2.08. 1 figure, 32 pages
dc.identifierhttps://arxiv.org/abs/math/0507521
dc.identifierhttp://arxiv.org/abs/math/0507521
dc.identifierJ. Algebra, 241 (2001), 340-378
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75895
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.subject16G99, 20G05, 20G10, 20G42
dc.titleThe Global Dimension of Schur Algebras for GL_2 and GL_3
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